DMRG Calculations of the Low-lying Excitations and Nonlinear Optical Properties of poly(para-phenylene)

A phenomenological two molecular orbital (2-MO) model of poly(para-phenylene) (PPP) is introduced. Its parameters are determined by fitting its predictions to exact Pariser-ParrPople model calculations of benzene and biphenyl, and it is solved using the density matrix renormalisation group method. It is shown that there exists a band of B u excitons below the band states. In the long chain limit the lowest exciton is situated 3.3 eV above the ground state, consistent with experimental data. The calculated particle-hole separation of these excitons indicates that they are tightly bound, extending over only a few repeat units. The lowest band state is found to be a covalent 21A+g state, whose energy almost coincides with the charge gap EG. Lying just above the 2 1 A + g state is a band 1 B − u state (the n 1 B − u state). The particle-hole separation of the band states scales linearly with oligomer size. The binding energy of the 1B u exciton is determined rigorously as 0.74 eV. The dipole matrix elements and oscillator strengths for the transitions between the lowest 1 A + g and 1 B − u states are calculated and the NLO properties of PPP, such as electroabsorption (EA) and third harmonic generation, are investigated. A comparison of the EA spectrum with the experimental data show that the main features of the experimental spectrum are well described in the 2-MO Hamiltonian. Only five states account for most of the calculated EA. These are the 11A+g , 1 1 B − u , 2 1 A + g , n 1 B − u and another band 1 A + g state, the k 1 A + g , thus confirming the essential states model. An analysis of the particle excitation weight of these states indicates that they are predominately single particle in character. PACS numbers: 42.70Jk, 71.20Rv, 78.66Qn, 71.35Cc